This paper presents a new generalized (or ray-pixel, raxel) camera calibration algorithm for camera systems involving distortions by unknown refraction and reflection processes. The key idea is use of intersections of calibration planes, while conventional methods utilized collinearity constraints of points on the planes. We show that intersections of calibration planes can realize a simple linear algorithm, and that our method can be applied to any ray- distributions while conventional methods require knowing the ray- distribution class in advance. Evaluations using synthesized and real datasets demonstrate the performance of our method quantitatively and qualitatively.